I wanted to know first off why the coils are coiled?
Suppose the wire is 10 m long. If you don't coil it, some of the heat it produces is "here" and some of the heat is 10 m away. Coiling it means you can heat a small area instead a long skinny area 10 m long.
when the coils are stretched too far apart thy run cold and when they are close together the run hot. What is the reason for this if resistance doesn’t change whether a wire is could or straight?
The temperature of the coils depends non only on how much heat they produce (\$I^2R\$) but also how much heat they lose to the environment. If you stretch the coil, it has an overall larger surface area over which heat is carried away by conduction and convection. If you compress the coil, it loses heat over a smaller area, and much of the heat produced by one turn of the coil actually heats the neighboring turns, rather than being lost to the environment.